Project 1: Innovative Biomarker-Integrated Clinical Trial Design and Analysis PROJECT SUMMARY With advances in biomedical technology, biomarkers are playing an increasingly important role in disease prog- nosis and treatment selection for cancer patients. Innovative clinical trial designs that incorporate biomarker information can improve study efficiency, require fewer patients, and reduce costs, thereby accelerating cancer drug development. The broad, long-term objective of this research project is to develop innovative statistical methodology to address issues in the design and analysis of biomarker-integrated clinical trials. There are four specific aims in this project. The first aim develops design and analysis methods to identify the optimal biomarker-based subgroups or the optimal biomarker cut-point for clinical trials with time-to-event endpoints. Statistical methods will be developed for both non-randomized and randomized trials. The second aim investi- gates a personalized treatment strategy that is adaptive to pre-randomization longitudinal biomarkers. Statistical methods based on selection models will be used to model longitudinal biomarkers and survival outcomes jointly. Sample size and power calculations for testing the interactions between longitudinal biomarkers and treatments will be developed. The third aim is to develop design and analysis methods for biomarker-enrichment clinical trials using surrogate-dependent and marker-dependent sampling. When the prevalence of marker positive pa- tients is low, the traditional design requires a large sample size, which can limit the feasibility of many studies. A new class of biomarker-based cost-effective designs will be studied and issues related to the implementation of the design, conditions for efficiency gain, and asymptotic properties of the new estimates will be investigated. Novel statistical measures for quantifying the benefit resulting from utilizing biomarkers to direct treatments will also be investigated. The fourth aim proposes two-phase clinical trials for discovering personalized predictive biomarkers. A two-phase design will be explored and sample size and power formulae for this two-phase design will be developed, especially for the novel second phase where auxiliary information from the first phase will be incorporated. For all of the aims, we will (1) investigate the theoretical properties of the proposed methodology based on modern empirical process theory and other advanced statistical theory; (2) examine the performance of the proposed methods in practical settings through extensive simulation studies; and (3) develop user-friendly software for the developed methods and for the sample size and power calculation tools and disseminate them freely to the general public.